Find the Product 2xy(3x^2-xy+7)

$2 x y (3 x^{2} - x y + 7)$

Step 1

Apply the distributive property.

$2 x y (3 x^{2}) + 2 x y (- x y) + 2 x y \cdot 7$

Step 2

Simplify.

Multiply $x$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

$2 (x^{2} x) y \cdot 3 + 2 x y (- x y) + 2 x y \cdot 7$

Multiply $x^{2}$ by $x$ .

Raise $x$ to the power of $1$ .

$2 (x^{2} x^{1}) y \cdot 3 + 2 x y (- x y) + 2 x y \cdot 7$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2 x^{2 + 1} y \cdot 3 + 2 x y (- x y) + 2 x y \cdot 7$

Add $2$ and $1$ .

$2 x^{3} y \cdot 3 + 2 x y (- x y) + 2 x y \cdot 7$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$2 x^{3} y \cdot 3 + 2 (x \cdot x) y (- 1 y) + 2 x y \cdot 7$

Multiply $x$ by $x$ .

$2 x^{3} y \cdot 3 + 2 x^{2} y (- 1 y) + 2 x y \cdot 7$

Multiply $7$ by $2$ .

$2 x^{3} y \cdot 3 + 2 x^{2} y (- 1 y) + 14 x y$

Step 3

Simplify each term.

Multiply $3$ by $2$ .

$6 x^{3} y + 2 x^{2} y (- 1 y) + 14 x y$

Multiply $y$ by $y$ by adding the exponents.

Move $y$ .

$6 x^{3} y + 2 x^{2} (y \cdot y) \cdot - 1 + 14 x y$

Multiply $y$ by $y$ .

$6 x^{3} y + 2 x^{2} y^{2} \cdot - 1 + 14 x y$

Multiply $- 1$ by $2$ .

$6 x^{3} y - 2 x^{2} y^{2} + 14 x y$